properly UV unwrapping "edge loop" geometry?
First remove doubles (W-->Remove Doubles) and apply transformations (Ctrl+A-->Apply Rotation, Scale). Then hide the non selected part of your mesh with Shift+H. Mark seams (select edges as pictured below and press Ctrl+E-->Mark Seam). Then select it with A and unwrap it U-->Unwrap.


Now straighten the UV islands ( How do I straighten UV maps? ).